Order-Disorder, Displacive Ferroelectrics, and use of Bragg CDI for characterization of Ferroelectric materials*

Nimish Nazirkar¹ and Edwin Fohtung<sup>1

1</sup>Department of Materials Sciences and Engineering, Rensselaer Polytechnic Institute, Troy, NY-12180

Ferroelectricity is observed in materials with non-centrosymmetric crystal structures having built-in Spontaneous Polarization. Ferroelectrics are broadly classified into three types: Displacive, Order-Disorder and electronic¹. Displacive Ferroelectricity relates to the movement of atoms in unit cells leading to spontaneous polarization². Order-Disorder ferroelectricity is related to the changes in phonon modes leading to shifts in bond lengths. Most of the time order-disorder ferroelectricity is followed by the displacement of atoms from equilibrium positions³. Bragg coherent diffraction imaging (BCDI)^4,5 a well-established technique for imaging the internal strain of nanoparticles, can be used to image the displacement of electron densities of the atoms. It can be used to relate displacement fields to the ferroelectric polarization in various ferroelectric materials using the Born-Effective Approximation and Landau Theory. 

References:

[1] http://abinitiomp.org/teaching/mtle6120/slides/insulators.pdf

[2] Wang, C., Wu, J., Zeng, Z. et al. Soft-mode dynamics in the ferroelectric phase transition of GeTe. npj Comput Mater 7, 118 (2021). https://doi.org/10.1038/s41524-021-00588-4

[3] Critical Role of Order-Disorder Behavior in Perovskite Ferroelectric KNbO₃. Zhi Tan, Yuting Peng, Jiao An, Qiming Zhang, and Jianguo Zhu. Inorganic Chemistry 2021 60 (11), 7961-7973.DOI: 10.1021/acs.inorgchem.1c00478

[4] Karpov, D., Liu, Z., Rolo, T. et al. Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field. Nat Commun 8, 280 (2017). https://doi.org/10.1038/s41467-017-00318-9

[5] Nanoscale topological defects and improper ferroelectric domains in multiferroic barium hexaferrite nanocrystals .D. Karpov, Z. Liu, A. Kumar, B. Kiefer, R. Harder, T. Lookman, and E. Fohtung Phys. Rev. B 100, 054432 – Published 22 August 2019